A shop owner and other witnesses said the soldier was shot in the head while buying digital video discs on Friday.
The US military had no immediate comment on the report.
The shop owner told Reuters two other soldiers came in and took him away after the shooting. It was not clear if the head wound was fatal.
The US command also said on Friday a US sailor attached to the first Marine Expeditionary Force has died in a "non-combat incident" in Iraq.
No further information was given.
The rise in attacks reflects the growing resentment among Iraqis against the presence of US and British forces in the country.
The US Central Command confirmed on Friday one of its soldiers was killed in an ambush near the town of Kufah, south of Baghdad overnight.
Centcom said the soldier, attached to the 1st Marine Expeditionary Force, was killed in an ambush while investigating a car theft near the town, close to the Shia holy city of Najaf, 130 kilometres south of Baghdad.
The attacks coincided with a search operation for two missing American soldiers who disappeared along with their Humvee vehicle on Wednesday.
US military intelligence believes the soldiers were abducted by Fedayeen militiamen in the town of Balad.
"They believe Fedayeen were using it (the Humvee), trying to get close to Americans with the vehicle to probably conduct another terrorist attack against them," Major Robert Twinner told AFP.
"The last time they spotted the vehicle was in Baghdad," he said.
A US officer said at least three people had been arrested on suspicion of being involved in the abduction.
In Balad, anti-US sentiments seemed to run high among the population which expressed a desire for a quick end of foreign military presence in Iraq.
Ali Abed, a 31-year-old farmer, said: "US forces are no longer welcome here. They are only here to control oil in the Middle East."
But the largest Shia group in Iraq has called for peaceful means to be used to bring about an end to occupation.
Ayatollah Mohammed Baqer al-Hakim, head of the Supreme Assembly for the Islamic Revolution in Iraq (SAIRI), said during his Friday sermon in Najaf that he opposed violence against US and British forces.
"We must start by negotiations and peaceful demonstrations against the occupation," Hakim said.
SAIRI is the main Shia group to have opposed Saddam's government and is part of a council of former opposition parties that has been in talks with the US about post-war Iraq's future administration.
More than 20 US troops have been killed in resistance operations in Iraq since US President George W. Bush declared major combat was over in May.